But it could be quite some time before a new version of that deal is formally set in motion, according to trade experts.

To renegotiate NAFTA, under a law passed in 2015, the White House must open an official 90-day negotiating window with Congress, during which time the legislative and executive branches will debate how the deal should be changed. That hasn't happened yet, according to congressional aides with knowledge of the process.

The White House is, however, pursuing informal negotiations, as evidenced by a meeting with leadership from the Senate Finance Committee and House Ways & Means Committee in early February. Press secretary Sean Spicer called the group — which included chief strategist Steve Bannon, presidential adviser Jared Kushner and the then-unconfirmed Commerce Secretary Wilbur Ross — an "all-star team" that would "chart the future of U.S. trade policy."

U.S. Customs and Border Protection officer directs trucks entering the United States from Mexico through the Otay Mesa Port of Entry in San Diego, California.

David Maung | Bloomberg | Getty Images

"The fact that the President met with Congressional leaders on Feb. 2 and discussed NAFTA renegotiation does not mean the U.S. clock has started," according to Ambassador Carla Hills, the primary NAFTA negotiator as U.S. Trade Representative under George H.W. Bush.

A senior Trump administration official called that meeting informal, saying the White House would pursue substantive changes in the deal through "proper channels." In the meantime, aides for the House Ways & Means committee and the Senate Finance committee — the groups with jurisdiction to rework trade agreements — told CNBC they had not received communication from the White House to do so before recess began this week.

The purpose of the 90-day period is to allow the Administration and Congress to "develop common goals," according to Ambassador Miriam Sapiro, a former deputy U.S. trade representative under President Barack Obama who today is with public relations firm Finsbury.

Mexico begins 'contingency plans'

Traditionally, the role of liaison between the White House and Congress would be served by the U.S. Trade Representative. Trump nominated Robert Lighthizer for the post, but there has yet to be a committee hearing scheduled.

Trump previously said trade policy would be led by Commerce Secretary Wilbur Ross and Peter Navarro, who helms a newly created trade council, but only the office of the USTR "has the resources to actually do the negotiation," according to Jeff Schott, senior fellow at the Peterson Institute for International Economics.